erate antibonding orbitals. (In filling degenerate orbitals, Hund’s rules still
apply.) Because of their symmetry properties, bonding orbitals have the “u”
label and antibonding orbitals have the “g” label for homonuclear diatomics.
The relative energy ordering ofand molecular orbitals from patomic
orbitals depends on the second-row atoms involved. For Li 2 through N 2 , the
ordering is ( (^) u 2 px, (^) u 2 py) g 2 pz( g 2 px, g 2 py) u 2 pz.For O 2 and F 2
(and Ne 2 , although this species does not exist as a stable molecule), the order-
ing of the bonding molecular orbitals is switched:g 2 pz( (^) u 2 px, (^) u 2 py)
( g 2 px, g 2 py) u 2 pz. How can we justify the difference in ordering of mo-
lecular orbitals? First of all, we note that for the smaller atoms, the 2sand 2p
orbitals are closer in energy than they are for the larger atoms of the second-
row atoms. By the reasoning above that only similar-energy atomic orbitals will
interact, the smaller atoms will have more interaction between the 2sorbitals
and the 2porbitals than the larger atoms. Because of that increased inter-
action, one resulting molecular orbital increases its energy and the other mo-
lecular orbital decreases its energy. In addition, not all three pairs of the
2 p-derived molecular orbitals will interact strongly with the 2sorbital—their
orientations aren’t right for good interaction. (This is a consequence of sym-
metry, which will be discussed in the next chapter.) Only one of the molecular
orbitals has the correct orientation and will interact, altering its expected energy.
This ultimately yields a relative ordering of molecular orbitals for Li 2 through
N 2 that differs from that in O 2 through Ne 2.
Perhaps the most obvious experimental observation in support of this
model of molecular wavefunctions is the diamagnetism of O 2 , caused by one
unpaired electron in each of the two degenerate *gmolecular orbitals. Figure
12.23 summarizes the occupancies of the molecular orbitals for diatomics of
the second-row elements.
For heteronuclear diatomics, the molecular orbital picture is similar, al-
though the energies of the atomic orbitals are no longer the same. Molecular
orbital diagrams show atomic orbitals at different levels on the vertical energy
scale, as shown in Figure 12.24 for NO and HF. Note in HF that two of the
originally degenerate patomic orbitals of F do not participate in the bonding
(by this approximation). Thus, they remain in doubly degenerate nonbonding
orbitals. The electron configuration of HF, ()^2 (2px^2 ,2py^2 ), does not have atomic
orbital labels for the doubly occupied bonding orbital making the inter-
nuclear bond. In this case, it is derived from the 1satomic orbital of H and the
2 pzatomic orbital of F.
12.14 Summary
Spin has dramatic consequences for the electronic structure of atoms. Because
of the Pauli principle, at most two electrons can fit in each orbital. Given the
restrictions on the and mquantum numbers, this requires that successive
shells about atoms be filled with successive electrons. This gives atoms size.If
the Pauli principle did not apply to electrons, they could all fit into a 1sH-like
orbital. But because only two of them can be allowed in each orbital, one of
each spin, larger and larger shells must be filled as the number of electrons in-
creases. Ultimately, the Pauli principle gives atoms their size.
There are no known analytic solutions to the Schrödinger equation for
systems more complex than the hydrogen atom. This does not imply that
quantum mechanics is not applicable to larger systems. Perturbation theory
12.14 Summary 413